TESTING/LIN/dtpt02.f(3)

okay so bestie, this is the manual page for TESTING/LIN/dtpt02.f(3) from the Library Functions Manual, and it's literally all about DTPT02. Buckle up, it's giving linear algebra but make it cute. 💖

💖 NAME

TESTING/LIN/dtpt02.f — yes, that's the whole name section. Iconic, lowkey. 💅

🌸 SYNOPSIS

🦋 Functions/Subroutines

   subroutine dtpt02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
       resid)

DTPT02

🧚 Function/Subroutine Documentation

   subroutine dtpt02 (character uplo, character trans, character diag, integer
       n, integer nrhs, double precision, dimension( * ) ap, double precision,
       dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, *
       ) b, integer ldb, double precision, dimension( * ) work, double
       precision resid)

DTPT02

✨ Purpose

Okay so DTPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the maximum over

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon. The norm used is the 1-norm. Slay. 💅

🎀 Parameters

• UPLO — is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• DIAG — is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — is INTEGER. The order of the matrix A. N >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — is DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
• X — is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — is DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — is DOUBLE PRECISION array, dimension (N).
• RESID — is DOUBLE PRECISION. The maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 140 of file dtpt02.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Footer vibes: source TESTING/LIN/dtpt02.f(3), version LAPACK Version 3.12.0 — and that's the footer, no extra date listed. No cap, you understood it, periodt. 💖✨🎀